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Pavlos Peppas

Publications and source records attributed to Pavlos Peppas.

2 recordsLinked to original sources

Auto-Relational Reasoning

Background & Objectives: In the last decade, Machine learning research has grown rapidly, but large models are reaching their soft limits demonstrating diminishing returns and still lack solid reasoning abilities. These limits could be surpassed through synergistic combination of Machine Learning scalability and rigid reasoning. Methods: In this work, we propose a theoretical framework for reasoning through object-relations in an automated manner integrated with Artificial Neural Networks. We present a formal analysis of the Reasoning, and we show the theory in practice through a paradigm integrating Reasoning and Machine Learning. Results: This paradigm is a system that solves Intelligence Quotient problems without any prior knowledge of the problem. Our system achieves 98.03% solving rate corresponding to the top 1% percentile or 132-144 iq score. This result is only limited by the small size of the model and the processing capabilities of the machine it run on. Conclusions: With the integration of prior knowledge in the system and the expansion of the dataset, the system can be generalized to solve a large category of problems. The functionality of the system inherently favors the solution of such problems in few-shot or zero-shot attempts.

cs.AI

Self-referential basis of undecidable dynamics: from The Liar Paradox and The Halting Problem to The Edge of Chaos

In this paper we explore several fundamental relations between formal systems, algorithms, and dynamical systems, focussing on the roles of undecidability, universality, diagonalization, and self-reference in each of these computational frameworks. Some of these interconnections are well-known, while some are clarified in this study as a result of a fine-grained comparison between recursive formal systems, Turing machines, and Cellular Automata (CAs). In particular, we elaborate on the diagonalization argument applied to distributed computation carried out by CAs, illustrating the key elements of Gödel's proof for CAs. The comparative analysis emphasizes three factors which underlie the capacity to generate undecidable dynamics within the examined computational frameworks: (i) the program-data duality; (ii) the potential to access an infinite computational medium; and (iii) the ability to implement negation. The considered adaptations of Gödel's proof distinguish between computational universality and undecidability, and show how the diagonalization argument exploits, on several levels, the self-referential basis of undecidability.

cs.LO